For what n do you have a winning strategy?

Is there an n for which you have a winning strategy in the modified case where your opponent can make

*any*move on her turn, while you are constrained to make legal king moves only?

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

Guest Message by DevFuse

Started by bonanova, Jan 29 2013 07:42 AM

7 replies to this topic

Posted 29 January 2013 - 07:42 AM

A king tours an nxn chessboard without visiting a square twice. Your opponent begins by placing the king in any corner. Thereafter, you and she alternate making legal moves of the king. A player loses when there is no previously unoccupied square available for a move.

For what n do you have a winning strategy?

Is there an n for which you have a winning strategy in the modified case where your opponent can make*any* move on her turn, while you are constrained to make legal king moves only?

For what n do you have a winning strategy?

Is there an n for which you have a winning strategy in the modified case where your opponent can make

- Bertrand Russell

Posted 29 January 2013 - 10:13 AM

Spoiler for For starters

Past prime, actually.

Posted 31 January 2013 - 11:42 AM

Spoiler for For starters

OK so far. How about n=8?

- Bertrand Russell

Posted 31 January 2013 - 04:34 PM

This is like a Tron game with diagonals. Nice to play. The strategy is get in the middle first.

Posted 01 February 2013 - 03:17 AM

I can’t find any simple formal description for the strategy. It appears, for an even “n” - you win; for an odd - she does.

Spoiler for Diagram

Interesting question is: with an even n, can __she__ have a winning strategy in the modified version, where she can jump the King to any available square?

Past prime, actually.

Posted 01 February 2013 - 05:32 AM

And then you must watch out for traps

Spoiler for a trap

Past prime, actually.

Posted 01 February 2013 - 03:27 PM

And then you must watch out for traps

Spoiler for a trap

Not really. Your next move is A6 and she loses.

Posted 01 February 2013 - 07:22 PM

And then you must watch out for traps

Spoiler for a trapNot really. Your next move is A6 and she loses.

True. My mistake.

Perhaps, the following could be thought of as a trap, though it's a stretch

Spoiler for a trap?

For any even n, you must win.

Past prime, actually.

0 members, 0 guests, 0 anonymous users